The invention relates generally to hysteresis synchronous motors, and in particular, to controlling hysteresis synchronous motors used in applications which require extremely constant rotational velocity.
Hysteresis synchronous motors can provide very constant rotational speed when driven from a crystal oscillator based input frequency. The operation of the motor is as follows. A pair of quadrature drive signals, which may be either square waves or sinusoidal, are applied to a pair of motor windings which form the stator of the motor. The alternating stator drive currents generate a magnetic field which rotates at the frequency of the stator drive signals.
The rotor is composed of a solid piece of ferrous material. The magnetic field from the energized stator windings induces a magnetic flux in the rotor thereby forming corresponding magnetic poles. The rotating magnetic field and the rotor magnetic field interact to generate a torque that causes the rotor and motor shaft to rotate. In response, the rotor accelerates until the angular velocity of the rotor matches that of the rotating magnetic field.
Any angular displacement between the rotating field and the rotor poles produces a restoring torque in the opposite direction. In response, the rotor velocity changes to reduce the angle thereby causing the rotor's frequency of rotation to match the frequency of the rotating field. It is this operation that provides the hysteresis motor with an excellent long term stability.
FIG. 1 shows a block diagram of an electromechanical model of a hysteresis synchronous motor. The motor can be modeled as a second order system. More specifically, the open loop gain of the motor is represented by equation 1 below: ##EQU1## where K.sub.m is a motor constant, J is the motor's inertia, B is a damping factor, and S is a Laplace variable. For a typical motor, these values can be: K.sub.m =0.049n.times.m/rad; J=1.times.10.sup.-4 kg.times.m.sup.2 ; and B=5.times.10.sup.-4 n.times.m.times.s/rad.
The closed loop motor transfer function is represented by equation 2 below: ##EQU2## where p.sub.i is a Phase input, and p.sub.o is a Phase output. In a more standard form, the closed loop motor transfer function is represented by equation 3 below: ##EQU3##
Unfortunately, the dynamic response of this type of motor is often underdamped, due to the low damping factor B, and the size of the inertia J. Thus, the rotor frequency tends to drift above and below the desired frequency (i.e., the frequency of the stator drive signals) as the rotor constantly attempts to match the desired frequency. For example, a rotor which spins at a nominal rate between 150-200 rotations per second typically "hunts" at a very low frequency of about 3 to 5 hertz around the nominal velocity. This hunting rate is referred to as the motor's "natural frequency" .omega..sub.n and is represented by equation 4 below: ##EQU4##
A feedback servo control device is typically used to reduce hunting and obtain an extremely constant rotational velocity. Toward this end, a tachometer or shaft encoder is connected to measure the instantaneous rotor frequency. A feedback servo controller monitors the measured rotor frequency and continuously adjusts the frequency of the stator drive signals in an effort to maintain the rotor frequency at a constant desired frequency.
In some applications, such a feedback servo controller is prohibitively expensive. Accordingly, if the frequency drift can be tolerated, a hysteresis synchronous motor is used without feedback control. However, if very high resolution is required, some mechanism must be used to eliminate or reduce the frequency drift inherent in a hysteresis synchronous motor. For example, laser scanners used in printing devices require high precision. The hunting of the motor produces artifacts which are easily visible to the eye. These artifacts in the printing (or scanning) process detract, from the image and provide a clearly less desirable result.
It is therefore an object of the present invention to provide a low-cost reliable, precise control mechanism to eliminate low frequency hunting in a hysteresis synchronous motor. Other objects of the invention are a method and apparatus employing existing equipment for controlling the synchronous motor in a precise manner.